A further contribution of the paper concerns the evaluation of VaR and ES in the context of portfolio optimization (see, e.g, [1]} and [2]}). blackIn recent years, the MAL density has attracted wide attention in the literature for its flexibility in modeling financial data ([3]}, [4]} and [5]}) and for its interesting properties that can be exploited to derive optimal portfolio allocations (see [6]} and [7]}). blackIn the classic Mean-Variance (MV) methodology of [8]}, portfolio risk is measured using the standard deviation of the portfolio. However, the MV approach is reasonably applicable only in cases where either returns follow a Gaussian distribution or the investors utility function is quadratic. Given the empirical evidence showing that market participants have a preference for positive skewness and they are more concerned about the downside risk (see [9]} and [10]} among others), the MAL distribution blackcould represents a more effective tool to select optimal portfolio allocations in the case of risk-averse agents.  blackTherefore, in this paper we exploit the MAL properties to incorporate skewness directly into the portfolio optimization method and to identify the optimal allocation weights. We then compute the corresponding portfolio VaR and ES as a function of the multivariate structure of the data. We prove how this result follows directly from blackthe fact that any linear combination of the MAL components is still AL distributed, with location, skew and scale parameters that are functions of the MAL parameters and the portfolio weights. Therefore, once we obtain the Maximum Likelihood (ML) estimates of the MAL parameters from the proposed dynamic quantile regression model, we fix a desired level of risk for any target portfolio and search for the optimal allocation weights according to the adopted strategy.
